Chapter 2, Problem 7RWDT

To determine

To find: An example of a function which is locally linear but not differentiable.

Explanation of Solution

Given information:

A function is locally linear.

Concept Used

Using local linearity, a function is differentiable at any point and closely resembles its own tangent line very close to that point. In the graph, differentiable curves will “straighten out” when we zoom in on them at a point of differentiability

Calculation:

Take an example of:

  $g=\sqrt{4-x^2}$

By the graph of $g=\sqrt{4-x^2}$:

  

  $g=\sqrt{4-x^2}$ is locally linear near $(-2,0)\text{and}\left(2,0\right)$ But the slope of tangent line at these points are infinite.

Therefore, the function is not differentiable at these points.